Question: Multiply the following complex numbers: $({-2i}) \cdot ({-4-3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2i}) \cdot ({-4-3i}) = $ $ ({0} \cdot {-4}) + ({0} \cdot {-3}i) + ({-2}i \cdot {-4}) + ({-2}i \cdot {-3}i) $ Then simplify the terms: $ (0) + (0i) + (8i) + (6 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 8)i + 6i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 8)i - 6 $ The result is simplified: $ (0 - 6) + (8i) = -6+8i $